The ability to analyse, interpret and evaluate statistical information

Communicating statistical information and understandings

Overview

In this activity you will see how you compare to other members of your class (and other Australian students of your year level) in terms of:

Height

Arm span

Foot length

Height of your belly button from the floor when standing

The CensusAtSchool questionnaire has questions that will be a useful source of information for your investigation. See Sections 8 and 9 below to find out more about the CensusAtSchool Questionnaire and Random Sampler prior to beginning this activity.

Requirements

Computer with internet connection

Spreadsheet software

Calculator

Pens and paper

Student Worksheet

Instructions

Instructions:

You will begin this activity by taking measurements of yourself and your classmates. Record the data in a table and then display the data in a histogram. From this you can decide how you compare to your class. You can also compare yourself and your class to students from across Australia by taking a data sample from CensusAtSchool.

Task One: Collect data about yourself and your class

1. Take the four measurements for yourself and record them in a table like the one below. Answer to the nearest half centimetre.

MEASUREMENTS FOR STUDENTS IN MY CLASS

Student*

Height (cm)

Arm Span (cm)

Belly Button (cm)

Right Foot (cm)

Me

Jack

Jill

Angelo

Tri

...............etc.

* You could identify students as Student1, Student2, Student3 etc. instead of using actual names

2. Add the measurements for your classmates to the table.

Task Two: Analyse the data using summary statistics3.Represent the height of the class by finding the mean for the Height column. Median and mode could also be used to represent the class.

Class Height Mean ___________

Median ___________

Mode ___________

(It will be easy to do if you put your data into an Excel spreadsheet and use the 'Insert Function' in the tool bar e.g. to find these values)

4. Look carefully at your analysis. Which one of mean, mode or median best represents your class? You might use more than one.

5. State how you compare to your class.
E.g. How are you similar or different?
(When you compare data you need to ask:
In which measures are you similar to your class?
In which measures are you different to your class?

Task Three: Display your data in a histogram

Graphs provide a visual representation of the data that can give a quick impression of the distribution. Grouped numerical data is best represented in a histogram. An example of a histogram is shown below: Note there are no gaps between the columns and the interval labels for the groups are at each edge of the column.

It is necessary to construct a table like this prior to drawing the histogram:

Interval

Tally

Frequency

0 -

IIII

5

100 -

I

1

110 -

0

120 -

II

2

130 -

IIIIIIII II

12

140 -

IIIIIIIIIIIIIIIIIIII IIII

29

150 -

IIIIIIIIIIIIIIIIIIII IIIIIIIIIIIIIIIIIIIIIIII

55

160 -

IIIIIIIIIIIIIIIIIIII IIIIIIIIIIIIIIII I

46

170 -

IIIIIIIIIIII IIIIIIIIIIIIIIII I

36

180 -

IIIIIIII II

12

190 -

II

2

6. Construct a frequency table then draw a histogram to represent the data in the Height column for your class.
This is best done using the Statistical Tools Add-in for Excel which will construct the table and histogram for you. If you don't have this Add-in on your version of Excel you will need to construct the table and draw the histogram by hand. Use a coloured line to indicate your own value in both the table and the chart.

7. What does the histogram tell you that the mean, mode and median don't tell you about how you compare to your class?

8. Repeat the steps above for the arm span, the belly button height and the right foot length.

Task Four: Comment on your results

9. Prepare a written summary that describes your class.Includeeach of the four measures and any findings you gain from your summary statistics and the histograms. Use this to describe a typical student in your class.

10. Are you a typical student for your class? If not how close to being typical are you?

Extension

How do you compare to Australian students?

This is the final part of your investigation in which you conduct a similar analysis on your sample of Australian students. This will enable you to describe Australian students from the Australian CensusAtSchool Project and see how you and your class compare.

11. Go to http://www.abs.gov.au/censusatschool, click on the Random Sampler link to get a sample of 100 Australian students of your year. You could take a sample for a particular state/territory, if you prefer. You can use data from CensusAtSchool Prepared Samples of numerical data.

Questions 13 to 16 will provide the data for the measurements you are investigating. Copy and paste only these 4 columns into a new worksheet.

12. Prepare a summary that describes your sample of Australian students. What does a typical Australian student look like?

13. How do you compare to a typical Australian student from the Australian CensusAtSchool Project?

14. How does a typical student for your class compare to a typical Australian student from the Australian CensusAtSchool Project?

15. Write a statement to explain any similarities and differences. For example, Why might there be height differences displayed in people from different parts of Australia? You could consider age, culture and gender.

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